Abstract
Self-organised regular pattern formation is one of the foremost examples of the development of complexity in ecosystems. Despite the wide array of mechanistic models that have been proposed to understand pattern formation, there is limited general understanding of the feedback processes causing pattern formation in ecosystems, and how these affect ecosystem patterning and functioning. Here we propose a generalised model for pattern formation that integrates two types of within-patch feedback: amplification of growth and reduction of losses. Both of these mechanisms have been proposed as causing pattern formation in mussel beds in intertidal regions, where dense clusters of mussels form, separated by regions of bare sediment. We investigate how a relative change from one feedback to the other affects the stability of uniform steady states and the existence of spatial patterns. We conclude that there are important differences between the patterns generated by the two mechanisms, concerning both biomass distribution in the patterns and the resilience of the ecosystems to disturbances.
Highlights
Pattern formation at the landscape scale is an established feature of many ecosystems across the world
These large aggregations of mussels form in intertidal regions, most notably in the Dutch Wadden Sea, and are often patterned, with dense clusters of mussels separated by regions of bare sediment
Previous modelling predicts that self-organisation into spatial patterns significantly increases the resilience of mussel beds to disturbances, relative to the resilience of spatially uniform mussel populations
Summary
Pattern formation at the landscape scale is an established feature of many ecosystems across the world. We make a quasi-steady-state assumption on the kinetics of s, setting s = P Q m in (2a,b) In order for this to be a good quantitative approximation, it would be necessary that P and Q are significantly larger than comparable rate parameters in other equations. This is not the case: the timescale of sediment production and erosion is broadly similar to that of mussel birth and death, and for example the values estimated by Liu et al (2012) for P and Q are the same. We give the rescalings in full because our subsequent work depends crucially on the way in which the (dimensional) algal supply rate affects
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